Application of the spectral density function method to a composite system

The spectral density representation of Bergman [Ann. Phys. 138 (1982) 78] is applied to measurements of bulk permittivity on a composite system with various levels of filler concentration, in order to extract structural information such as shape and spatial arrangement of the filler particles. The composites are paraffin wax filled with metal-coated hollow glass micro-spheres. The inclusions have an outer layer of dielectric which prevents conduction between them. In the spectral density analysis, the dielectric permittivity of the matrix phase is used as measured. The permittivity of the particles is deduced by application of a mixture formula to the measured permittivity of the composite system with low concentrations of filler. The calculated spectral density functions for each concentration level indicate that the topology of the mixtures undergoes a transition when the inclusion concentration reaches approximately 25%.